A cantilever beam with a rectangular cross section with elastic modulus \( E \), is fixed at the left end and subjected to a moment M about the x -axis, as shown in the figure. The cross section of the beam has width b (in the z -direction) and height, h (in the y -direction).
- Use a free body diagram to determine the internal moment
- Find the moment of inertia about the z-axis, \( I_{z} \) in terms of b and h
- Determine the maximum and minimum bending stresses \( \sigma_{b}^{\max }=\sigma_{t}, \sigma_{b}^{\min }=\sigma_{c} \) in terms of \( \mathrm{b}, \mathrm{h} \), and M
- Determine the associated strains due to bending